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DOE OSTI2022

Generalized design principles for hydrodynamic electron transport in anisotropic metals

Interactions of charge carriers with lattice vibrations, or phonons, play a critical role in unconventional electronic transport of metals and semimetals. Recent observations of phonon-mediated collective electron flow in bulk semimetals, termed electron hydrodynamics, present new opportunities in the search for strong electron-electron interactions in high carrier density materials. Here we present the general transport signatures of such a second-order scattering mechanism, along with analytical limits at the Eliashberg level of theory. We study electronic transport, using ab initio calculations, in finite-size channels of semimetallic ZrSiS and TaAs 2 with and without topological band crossings, respectively. The order of magnitude separation between momentum-relaxing and momentum-conserving scattering length scales across a wide temperature range make both of them promising candidates for further experimental observation of electron hydrodynamics. More generally, our calculations suggest that the hydrodynamic transport regime does not, to first order, rely on the topological nature of the bands. Finally, we discuss general design principles guiding future search for hydrodynamic candidates, based on the analytical formulation and our ab initio predictions. Further, we find that systems with strong electron-phonon interactions, reduced electronic phase space, and suppressed phonon-phonon scattering at temperatures of interest are likely to feature hydrodynamic electron transport. We predict that layered and/or anisotropic semimetals composed of half-filled d shells and light group V/VI elements with lower crystal symmetry are promising candidates to observe hydrodynamic phenomena in the future.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Characterisation of nano-assemblies inside mesopores using neutron scattering

Adsorption of molecular and nanoscale matter in mesoporous materials is important in filtration and chromatography as well as membrane processes. However, the morphology and distribution of self-assembled structures of adsorbate formed within nanoconfined environments is largely unknown. Small Angle Neutron Scattering (SANS) with porous matrix matching the neutron scattering length density of the solvent has the potential to provide detailed information on the self-assemblies formed in pore spaces. However, analysis of such SANS profiles remains a challenge. In this study, we extend the SANS analysis method previously developed by Findenegg and co-workers to include interparticle correlations, providing a qualitative characterisation of the adsorption state of surfactants and nanoparticles in the cylindrical pores of silica nanomaterials. We find that the pore filling fraction and the self-assembled state of the adsorbate governs the scattering profile. We apply the model to two materials namely, triethyleneglycol monohexyl ether (C 6 E 3 ) surfactant and gold nanoparticles adsorbed in SBA-15 mesoporous silica. In contrast to the C 6 E 3 system, Bragg scattering dominates the diffuse scattering in gold nanoparticle system, which we attribute to the immobile internal structure of the nanoparticles. In conclusion, this new SANS analysis method has potential to elucidate structures of soft matter nanoassemblies inside mesopores.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Design of a Thomson scattering diagnostic for the SMall Aspect Ratio Tokamak (SMART)

Here, we describe the design of a Thomson scattering (TS) diagnostic to be used on the SMall Aspect Ratio Tokamak (SMART). SMART is a spherical tokamak being commissioned in Spain that aims to explore positive triangularity and negative triangularity plasma scenarios at a low aspect ratio. The SMART TS diagnostic is designed to operate at high spatial resolution, 6 mm scattering length in the low-field side and 9 mm in the high-field side regions, and a wide dynamic range, electron temperature from 1 eV to 1 keV and density from 5 x 10 18 m -3 to 1 x 10 20 m -3 ⁠, to resolve large gradients formed at the plasma edge and in the scrape-off layer (SOL) under different triangularities and low aspect ratios. A 2 J @1064 nm laser will be used that is capable of operating in the burst mode at 1, 2, and 4 kHz to investigate fast phenomena and at 30 Hz to study 1 s (or more) long discharges. The scattered light will be collected over an angular range of 60° – 120° from 28 spatial points in the midplane covering the entire plasma width and the outer midplane SOL. Each scattering signal will be spectrally resolved on five wavelength channels of a polychromator to obtain the electron temperature measurement. We will also present a method to monitor in situ laser alignment in the core during calibrations and plasma operations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

On two nucleons near unitarity with perturbative pions

We explore the impact of perturbative pions on the Unitarity Expansion in the two-nucleon S-waves of Chiral Effective Field Theory at next-to-next-to leading order (N 2 LO). Pion exchange explicitly breaks the nontrivial fixed point’s universality, i.e. invariance of S waves under both conformal and Wigner’s combined SU(4) spin–isospin transformations. On the other hand, Unitarity explicitly breaks chiral symmetry. The two seem incompatible in their respective exact-symmetry limits. χEFT with Perturbative Pions in the Unitarity Expansion resolves the apparent conflict in the Unitarity Window (phase shifts 45° ≲ δ(k) ≲ 135°), i.e. around momenta most relevant for low-energy nuclear systems. Its only LO scale is the scattering momentum; NLO adds only scattering length, effective range and non-iterated one-pion exchange (OPE); and N 2 LO only once-iterated OPE. Agreement in the 1 S 0 channel is very good.

Chiral symmetry↗

DOE OSTI2020

Neutron sub-micrometre tomography from scattering data

Neutrons are valuable probes for various material samples across many areas of research. Neutron imaging typically has a spatial resolution of larger than 20 µm, whereas neutron scattering is sensitive to smaller features but does not provide a real-space image of the sample. A computed-tomography technique is demonstrated that uses neutron-scattering data to generate an image of a periodic sample with a spatial resolution of ∼300 nm. The achieved resolution is over an order of magnitude smaller than the resolution of other forms of neutron tomography. This method consists of measuring neutron diffraction using a double-crystal diffractometer as a function of sample rotation and then using a phase-retrieval algorithm followed by tomographic reconstruction to generate a map of the sample's scattering-length density. Topological features found in the reconstructions are confirmed with scanning electron micrographs. This technique should be applicable to any sample that generates clear neutron-diffraction patterns, including nanofabricated samples, biological membranes and magnetic materials, such as skyrmion lattices.

nanoscience↗

DOE OSTI2024

Elastic scattering of 3 He + 4 He with the SONIK scattering chamber

Measurements of the elastic scattering cross section of 3 He and 4 He are important in order to improve constraints on theoretical models of 4 He ⁢( 3 He ,𝛾)⁢ 7 Be, a key reaction in Big Bang nucleosynthesis and solar neutrino production. The astrophysical 𝑆 factor for this reaction is a significant source of uncertainty in the standard-solar-model prediction of the 7 Be and 8 B solar neutrino fluxes. The elastic scattering measurements reported in the literature do not extend to low energies and lack proper uncertainty quantification. A new measurement of the 4 He ⁢( 3 He, 3 He)⁢ 4 He reaction has been made at center-of-mass energies 𝐸c.m.=0.38−3.13 MeV using the Scattering of Nuclei in Inverse Kinematics (SONIK) scattering chamber: a windowless, extended gas target surrounded by an array of 30 collimated silicon charged particle detectors situated at TRIUMF. This is the first elastic scattering measurement of 3 He + 4 He made below 500 keV and it has greater angular range and better precision than previous measurements. The elastic scattering data were analyzed using both 𝑅-matrix and halo effective field theory frameworks, and values of the 𝑠-wave scattering length and effective range were extracted. Here, the resulting improvement in knowledge of the 𝑠-wave effective-range function at low energies reduces the overall uncertainty in 𝑆 34 at solar energies.

Elastic scattering reactions↗

DOE OSTI2020

S -factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $

Previous studies of the reaction ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ have mainly focused on providing the best central value and error bar for the S factor at solar energies. Experimental measurements of this capture reaction at higher energies, the ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$ and its excited state, have been used to constrain the theoretical models employed for this purpose. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ to perform the extrapolation. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic properties of ${}^{7}\mathrm{Be}$ and its excited state, and short-distance contributions to the E1 capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total S factor $S(0)\,={0.577}_{-0.016}^{+0.015}$ keV b, while the branching ratio for excited- to ground-state capture at zero energy, ${Br}(0)={0.406}_{-0.011}^{+0.013}$, both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value $S(0)=0.56\pm 0.03\,\,\mathrm{keV}$ b, but has a smaller error bar. We also find significant constraints on ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering parameters, and we obtain constraints on the angular distribution of capture gamma rays, which is important for interpreting experiments. The path forward for this reaction seems to lie with better measurements of the scattering phase shifts and S(E)'s angular dependence away from zero energy, together with better understanding of the asymptotic normalization coefficients of the ${}^{7}$Be bound states' wave functions. Lastly, data on these could further reduce the uncertainty on S(0).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Backbone Stitching in Bottlebrush Copolymer Mesodomains and the Impact of Side Chain Crystallization

We synthesized bottlebrush statistical copolymers (BSCPs) having poly(ethylene oxide) (PEO) and poly(dimethylsiloxane) (PDMS) side chains attached to a polynorbornene backbone. Small-angle X-ray scattering analysis showed that for densely grafted BSCPs, the scattering length density gradually transitions between the PEO and PDMS domains. For loosely grafted BSCPs, the polymer backbone formed a distinct mesodomain, with a lower electron and mass density than both the PEO and PDMS domains. The bottlebrush backbone essentially “stitches” the PEO and PDMS side chains, looping back and forth from the PEO to PDMS domains with the backbone segments oriented normal to the domain interfaces. Self-consistent field theory (SCFT) calculations validated the stitching of the backbone driven by the microphase separation of PEO and PDMS, along with a strong segmental order of the side chains in the melt. The reduced birefringence upon PEO crystallization suggests the disruption of the strong segmental order by the crystallization. Both the static intrinsic and the form birefringences of the BSCPs decreased upon PEO crystallization. Solid-state NMR confirmed the rigidity of PEO crystallites and the bottlebrush backbone. Self-assembly of BSCPs containing polyhedral oligomeric silsesquioxane (POSS) pendent groups was also evaluated by X-ray scattering, showing the formation of lamellar microdomains that inhibited POSS crystallization.

Hu, Mingqiu↗

DOE OSTI2023

Analytic continuation of the relativistic three-particle scattering amplitudes

We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the nonrelativistic three-body scattering theory, we provide a detailed and general prescription for solving and analytically continuing integral equations describing the three-body reactions. We use these techniques to study a system with zero angular momenta described by a single scattering length leading to a bound state in a two-body subchannel. We obtain bound-state-particle and three-particle amplitudes in the previously unexplored kinematical regime; in particular, for real energies below elastic thresholds and complex energies in the physical and unphysical Riemann sheets. We extract positions of three-particle bound-states that agree with previous finite-volume studies, providing further evidence for the consistency of the relativistic finite-volume three-body quantization conditions. We also determine previously unobserved virtual bound states in this theory. Lastly, we find numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of the left-hand cuts and argue for the generalization of the existing formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Structure of diopside, enstatite, and magnesium aluminosilicate glasses: A joint approach using neutron and x-ray diffraction and solid-state NMR

Neutron diffraction with magnesium isotope substitution, high energy x-ray diffraction, and 29 Si, 27 Al, and 25 Mg solid-state nuclear magnetic resonance (NMR) spectroscopy were used to measure the structure of glassy diopside (CaMgSi 2 O 6 ), enstatite (MgSiO 3 ), and four (MgO) x (Al 2 O 3 ) y (SiO 2 ) 1–x–y glasses, with x = 0.375 or 0.25 along the 50 mol. % silica tie-line (1 – x – y = 0.5) or with x = 0.3 or 0.2 along the 60 mol. % silica tie-line (1 – x – y = 0.6). The bound coherent neutron scattering length of the isotope 25 Mg was remeasured, and the value of 3.720(12) fm was obtained from a Rietveld refinement of the powder diffraction patterns measured for crystalline 25 MgO. The diffraction results for the glasses show a broad asymmetric distribution of Mg–O nearest-neighbors with a coordination number of 4.40(4) and 4.46(4) for the diopside and enstatite glasses, respectively. As magnesia is replaced by alumina along a tie-line with 50 or 60 mol. % silica, the Mg–O coordination number increases with the weighted bond distance as less Mg 2+ ions adopt a network-modifying role and more of these ions adopt a predominantly charge-compensating role. 25 Mg magic angle spinning (MAS) NMR results could not resolve the different coordination environments of Mg 2+ under the employed field strength (14.1 T) and spinning rate (20 kHz). The results emphasize the power of neutron diffraction with isotope substitution to provide unambiguous site-specific information on the coordination environment of magnesium in disordered materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

$K^0_S$ and $Λ(\overline{Λ})$ two-particle femtoscopic correlations in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02TeV

Two-particle correlations are presented for $K^0_S$, $Λ$, and $\overline{Λ}$ strange hadrons as a function of relative momentum in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset corresponds to an integrated luminosity of 0.607 nb -1 and was collected using the CMS detector at the CERN LHC. These correlations are sensitive to quantum statistics and to final-state interactions between the particles. The source size extracted from the $K^0_S$$K^0_S$ correlations is found to decrease from 4.6 to 1.6 fm in going from central to peripheral collisions. Strong interaction scattering parameters (i.e., scattering length and effective range) are determined from the $ΛK^0_S$ and $ΛΛ$ (including their charge conjugates) correlations using the Lednický–Lyuboshitz model and are compared to theoretical and other experimental results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Constrained Extrapolation Problem and Order-Dependent Mappings

In this work, we consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. Here, we find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Determining the leading-order contact term in neutrinoless double β decay

We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe - e - amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $ p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) $ , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ( NN ) scattering in the 1 S 0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1 S 0 NN scattering lengths. While our analysis is performed in the $ \overline{\mathrm{MS}} $ scheme, we express our final result in terms of the scheme-independent renormalized amplitude $ {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) $ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for $ {\mathcal{A}}_{\nu } $ , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Interactions of πK, ππK and KKπ systems at maximal isospin from lattice QCD

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically $π^+K^+, π^+π^+K^+$ and $K^+K^+π^+$. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS $N_f$ = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the $π^+π^+$ and $K^+K^+$ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit twoparticle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in $π^+π^+K^+$ and $K^+K^+π^+$ systems, finding statistically significant nonzero results in most cases. We include s and $\textit{p}$ waves in the K matrix for $π^+K^+$ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Refining internal bilayer structure of bicelles resolved by extended-q small angle X-ray scattering

The internal profile across the bilayer reveals important structural information regarding the crystallinity of acyl chains or the positions of encapsulated species. Here, we demonstrate that a simple five-layer-core-shell discoidal model can be employed tobest fit the extended-qsmall angle X-ray scattering (SAXS) data and resolvethe bilayer internal structure (with sub-nanometer resolution) of a nanoscale discoidal system comprised of a mixture of long-and short-chain lipids(known as “bicelles”). In contrast to the traditional core-shell discoidal model, the detailed structure in the hydrophobic core such as the methylene and methyl groups can be distinguished via this model. The refined model is validated by the SAXS data of bicelles whose electron scattering length density of the hydrophobic core is adjusted by the addition of a long-chain lipid with a fluorine-end group.The higher resolution of the bilayer internal structure can be employed to advance our understanding of the interaction and conformation of the membrane and associated molecules, such as membrane-associated proteins and locations of entrapped species in the lipid nanoparticles.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Crystal structure of the $τ_{11}$ Al 4 Fe 1.7 Si phase from neutron diffraction and ab initio calculations

The intermetallic τ 11 Al 4 Fe 1.7 Si phase is of interest for high-temperature structural application due to its combination of low density and high strength. We determine the crystal structure of the τ 11 phase through a combination of powder neutron diffraction and density functional theory calculations. Using Pawley and Rietveld refinements of the neutron diffraction data provides an initial crystal structure model. Since Al and Si have nearly identical neutron scattering lengths, we use density-functional calculations to determine their preferred site occupations. The τ 11 phase exhibits a hexagonal crystal structure with space group P6 3 /mmc and lattice parameters of a = 7.478 Å and c = 7.472 Å. The structure comprises five Wyckoff positions; Al occupies the 6h and 12k sites, Fe the 2a and 6h sites, and Si the 2a sites. Here we observe site disorder and partial occupancies on all sites with a large fraction of 80% Fe vacancies on the 2d sites, indicating an entropic stabilization of the τ 11 phase at high temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Evaluation of light collection from highly scattering media using wavelength-shifting fibers

Opaque scintillators are designed to have a short scattering length such that scintillation photons are probabilistically confined to a small region of space about their origin. The benefit of this feature is that information on the interaction event topology can be recorded with greater fidelity than in traditional highly transparent media with sensors at large distances from the light production region. Opaque scintillator detectors rely on wavelength-shifting fibers to extract the scintillation light; however, the efficiency of light collection has not yet been directly measured in experiment. We measured the efficiency of light collection as a function of the optical parameters of an opaque liquid and the distance from the origin of the light to the fiber. We use the experimental data to validate a Monte Carlo model of light transport and collection and discuss a simple diffusion model that reproduces the results of Monte Carlo simulation with high fidelity. Furthermore, this combination of validated models has the potential for use in predictions of performance in various designs of future opaque scintillator detectors such as LiquidO.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Study of the interaction between $Ξ$ baryons and light mesons via femtoscopy at the LHC

Meson-baryon systems with strangeness content provide a unique laboratory for investigating the strong interaction and testing theoretical models of hadron structure and dynamics. In this work, the measured correlation functions for oppositely charged $Ξ$-K and $Ξ$ − 𝜋 pairs obtained in high-multiplicity pp collisions at $\sqrt{𝑠}$ = 13 TeV at the LHC are presented. For the first time, high-precision data on the $Ξ$-K interaction are delivered at small relative momenta. The scattering lengths, extracted via the Lednický–Lyuboshits expression of the pair wavefunction, indicate a repulsive and a shallow attractive strong interaction for the $Ξ$-K and $Ξ$ − 𝜋 systems, respectively. The $Ξ$(1620) and $Ξ$(1690) states are observed in the $Ξ$ − 𝜋 correlation function and their properties, mass and width, are determined. These measurements are in agreement with other available results. Such high-precision data can help refine the understanding of these resonant states, provide stronger constraints for chirally motivated potentials, and address the key challenge of describing the coupled-channel dynamics that may give rise to molecular configurations .

Femtoscopy↗